NSF PAR Search | NSF Public Access Repository

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

The universal behavior of modulated stripe patterns

https://doi.org/10.1016/j.physd.2023.133688

Newell, Alan C; Venkataramani, Shankar C (May 2023, Physica D: Nonlinear Phenomena)

Full Text Available
An SBV relaxation of the Cross-Newell energy for modeling stripe patterns and their defects

https://doi.org/10.3934/dcdss.2022101

Venkataramani, Shankar C. (January 2022, Discrete and Continuous Dynamical Systems - S)

We investigate stripe patterns formation far from threshold using a combination of topological, analytic, and numerical methods. We first give a definition of the mathematical structure of 'multi-valued' phase functions that are needed for describing layered structures or stripe patterns containing defects. This definition yields insight into the appropriate 'gauge symmetries' of patterns, and leads to the formulation of variational problems, in the class of special functions with bounded variation, to model patterns with defects. We then discuss approaches to discretize and numerically solve these variational problems. These energy minimizing solutions support defects having the same character as seen in experiments.
more » « less
Full Text Available
Computing with non-orientable defects: Nematics, smectics and natural patterns

https://doi.org/10.1016/j.physd.2020.132828

Zhang, Chiqun; Acharya, Amit; Newell, Alan C.; Venkataramani, Shankar C. (March 2021, Physica D: Nonlinear Phenomena)
null (Ed.)
Full Text Available
Disk galaxies and their dark halos as self-organized patterns

https://doi.org/10.1016/j.physletb.2020.136060

Venkataramani, Shankar C.; Newell, Alan C. (February 2021, Physics Letters B)
null (Ed.)
Full Text Available
Pattern dark matter and galaxy scaling relations: Is dark matter the self-organized behavior and manifestation of things we already knew?

https://doi.org/10.1140/epjs/s11734-021-00196-9

Venkataramani, Shankar C.; Newell, Alan C. (January 2021, The European Physical Journal Special Topics)
null (Ed.)
Full Text Available

Search for: All records